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The North's leader Kim Jong-Un declared the test-launch of the Hwasong-15 missile a success, according to an announcement on state television.
North Korean state television brought out Ri Chun-Hee, a senior broadcaster who only appears for significant developments, to announce the landmark.
"Kim Jong Un declared with pride that now we have finally realised the great historic cause of completing the state nuclear force, the cause of building a rocket power," she said.
"The great success in the test-fire of ICBM Hwasong-15 is a priceless victory won by the great and heroic people of the DPRK," she said, using the official abbreviated name for North Korea.
Wednesday's missile was more sophisticated than any previously tested, state media said.
"The ICBM Hwasong-15 type weaponry system is an intercontinental ballistic rocket tipped with super-large heavy warhead which is capable of striking the whole mainland of the US," the official news agency KCNA said.
Pyongyang said the missile reached an altitude of 4,475 kilometres (2,800 miles) and had splashed down 950 kilometres from its launch site.
At least one Western expert said the missile's lofted trajectory suggested an actual range of 13,000 kilometres -- longer than that of any previous test and one that would extend to every major US city.
Trump, who recently announced fresh sanctions on Pyongyang and returned it to a US list of state sponsors of terror, was opaque in his immediate response, as the UN Security Council agreed to meet in emergency session.
"I will only tell you that we will take care of it," Trump said at the White House. "It is a situation that we will handle," he added, without elaborating.
US Secretary of State, Rex Tillerson, stressed that diplomatic options to resolving the crisis remained "viable and open."